The science of traffic physics is a new field emerging at the boundary of agent-based modeling and statistical physics. It addresses the statistical properties of large numbers of self-propelled objects acting on their own behalf. To date, the science has largely been applied to roadway vehicle dynamics because of the significant societal and financial import and because the problem is simplified by geometrical constraints. In addition, road traffic systems offer ready access to large amounts of data. This research has applicability to other many-agent systems in addition to roadways. The utility of the science is the ability to define systemic measures that are independent of the particular behaviors of each agent in a traffic system and independent of details of the system itself (such as geometric characteristics), much as the pressure exerted by a gas on its container is independent of the details of motion of each individual molecule in the gas and independent of the shape of the container.
Physical systems consisting of many particles are often characterized in terms of phase, such as liquid, solid, or gaseous. The phase is a property of an entire system, rather than of any of its particular components. Systems of interacting agents in freeway traffic have been shown both theoretically and empirically to exhibit phases that correspond to free-flowing (“liquid”) or jammed (“solid”) traffic. Traffic also has phases that do not have analogues in common physical systems, such as backwards-flowing waves of stalled traffic mixed with moving traffic.
If a system has more than one phase, it will have boundaries between phases. Varying a control parameter (such as temperature moving water from ice to liquid) can generate a phase transition. In purely physical systems, control parameters are usually external, though in engineered or biological systems they can be internal and adaptive. The set of phenomena around phase transitions are called critical phenomena, and include the divergence of the correlation length, ergodicity breaking (not all possible states of the system reachable from a given configuration), and other phenomena. The divergence of the correlation length is of particular interest in traffic systems because it means that a perturbation in one part of a system can affect another part at a large distance, with implications for controlling methodologies.
Just as molecules obey certain laws (conservation of energy and momentum and the equipartition of energy), the traffic “molecules” (agents representing vehicles with drivers) obey simple laws implemented in a fully distributed fashion—attempting to get where they are going as quickly as possible (with an upper limit) and interacting with other vehicles, such as avoiding collisions and following at a safe distance. Even though systems of self-propelled entities do not obey the same conservation laws as traditional equilibrium statistical systems do, many of the traffic physics systems that have been recently proposed have mappings onto well-studied equilibrium systems.
An example of this is the highly simplified collective motion model of Vicsek et. al., (T. Vicsek, A. Czirok, E. Ben Jacob, I. Cohen, and O. Schochet, “Novel type of phase transitions in a system of self-driven particles”, Physical Review Letters, Vol. 75 (1995), pp. 1226-1229) inspired by the computer graphics work of Reynolds (C. Reynolds, “Flocks, birds, and schools: a distributed behavioral model”, Computer Graphics, Vol. 21 (1987), pp. 25-34). Their model consists of a collection of entities all traveling at the same invariant speed in two dimensions but whose headings are allowed to vary. At each update cycle of the model, the directions of the particles are updated by the following rule: The direction is updated by taking the average of the directions of the neighboring particles in a radius r and adding a noise term. vi(t+1)=v(t)r+θi. The end result is a textbook phase transition as depicted in FIG. 1 which illustrates the relationship between Phase Transitions and Noise, where the y-axis denotes average alignment of particles, the x-axis denotes noise.
At low noise values (η), the entire system tends to align. As noise increases, uncorrelated motion results. As the system size becomes larger (the multiple curves shown) the curves asymptote to a single curve, another classic indicator of phase transition behavior. If one approaches the phase boundary from the high-noise side (large values of η) then there is a sudden emergence of preferred direction in the model; this is the phase transition boundary. As the system size approaches infinity, the onset of preferred direction becomes infinitely sharp.
A somewhat more realistic model than the previous one has been developed by Helbing (D. Helbing, “Traffic and related self-driven many-particle systems”, Reviews of Modern Physics, Vol. 73, 2001, pp. 1067-1141; D. Helbing, et al., “Micro- and macro-simulation of freeway traffic”, Mathematical and Computer Modeling, Vol 35, 2002, pp. 517-47) and others and corroborated with simulation and empirical data. In vehicle traffic, throughput (or capacity) of a roadway increases with density to a certain point after which a marked decrease is observed; hence, the emergence of a traffic jam. In this model the driving parameter is vehicle density per length of roadway, not noise. The two models and their effects are related: The higher the density the greater the frequency of correcting behavior (speeding up, slowing down). Each incidence of correcting behavior is associated with uncertainty (noise). Instead of the noise being applied externally, it is endogenously generated by adaptive agent behavior. When density is low, overshoots and undershoots do not propagate very far because of the “slack” in the system.
At a certain critical point, these perturbations ricochet throughout the system, generating a cascade of corrections and pushing the system into a radically different configuration (the “traffic jam” phase). The noise generated with each speed correction creates an equal or greater number of other speed corrections and the system cannot stably return to the initial configuration. This generates a phase transition. FIG. 2 illustrates a plot of a freeway traffic phase diagram in which the dotted line represents theoretical prediction for pure truck traffic, the solid line represents pure automobile traffic, and the black crosses indicate simulation results for mixed traffic, and the grey boxes indicate actual freeway measurements.
In prior art, systems and methods for separating aircraft has been limited to the use of radar, radio, conflict-probe and other software, and air traffic controller instructions to aircraft. The limitation of the past method is that it does not allow for management of trajectories based on the probabilities of future conditions in the airspace. Extending the traffic physics paradigm to the airspace problem requires some modifications and extensions to the current models in the literature. For the most part, aircraft have intent, and this factor needs to be reflected in any realistic model of the airspace. The Helbing model discussed above effectively incorporates intent, as the particles are constrained to move in one dimension, with intent to reach another location. The Vicsek model, though it has similarities to flight models, does not incorporate intent because there is no preferred direction of motion. Due to iterated directional corrections and the influence of noise, the initial direction of a particle may change by a large amount over time, and there is no notion of the initial (or any a priori) direction being “preferred” or “optimal”, though the model spontaneously generates preferred direction under the right parameter settings.
Accordingly, a need exists for an air traffic control system and technique that incorporates intent in a natural and computationally efficient way.
A further need exists for a system and technique to predict phase behaviors in an airspace.
Another need exists for the ability to develop a traffic physics/phase transition description and algorithmic measures to predict when an airspace will approach the limits of its capacity.
Still a further need exists for a system and technique to control an airspace phase state through management of bulk properties of many trajectories simultaneously.
Yet another need exists for the ability to identify effective approaches for separation assurance for aircraft trajectories (as contrasted with separation for aircraft only) in an airspace.
A still further need exists for algorithms, agent-based structures and methods for analyzing and managing the complexity of airspace states, while maintaining or increasing safety, involving large numbers of heterogeneous aircraft trajectories.
Additionally, a need exists for continuous replanning of flight paths so as to continually adjust all future flight paths to take into account current and forecast externalities as knowledge of these forecasts become available.
Finally, the need exists for this continuous replanning to be accomplished at computing speeds many times faster than real time, so as to complete the replanning in sufficient time to implement air traffic control adjustments in advance of the predicted unwanted phase behaviors.